CAIRO, Feb 6 (Reuters) - Egyptian liberal politician Mohamed ElBaradei condemned Egypt's Islamist-led authorities on Wednesday for not arresting a Muslim cleric who said he should be sentenced to death.

ElBaradei's response came the same day as an outspoken secular opponent of Tunisia's Islamist-led government was killed outside his home in what the country's prime minister condemned as a political assassination.

The "Arab Spring" revolts have brought emboldened Islamist parties to power after decades of repression, but have also exposed divisions between them and their secular opponents.

An online video clip of Egypt's religious al-Hafez channel showed hardline Salafi Muslim cleric Mahmoud Shaaban saying leaders of the main opposition coalition, the National Salvation Front, would be condemned to death under Islamic law, or sharia.

The NSF has been calling for regular protests against President Mohamed Mursi, the Muslim Brotherhood politician elected in June. He is accused by the opposition of trying to monopolise power.

Shabaan said the NSF leadership wanted power and were "burning Egypt" to get it. "It is clear now their sentence in God's law is death," he said in the video, which was posted on YouTube on Feb. 2.

The National Salvation Front leadership includes ElBaradei and former presidential candidates Amr Moussa and Hamdeen Sabahy. Shaaban named both Sabahy and ElBaradei in the video.

"When the 'sheikhs' issue fatwas on the necessity of killing in the name of religion without being arrested, say goodbye to the regime and the state. Oh, how many crimes are committed against Islam and in its name!" ElBaradei responded on Twitter.

In a separate Tweet in English, he wrote: "Regime silent as another fatwa gives license to kill opposition in the name of Islam. Religion yet again used and abused."

In both Egypt and Tunisia, many who campaigned to bring down autocratic rulers now feel their revolutions have been hijacked by Islamists.

The recently-elected Mursi, a member of the Muslim Brotherhood, has seen resentment rise across Egypt over what demonstrators see as his attempts to monopolise power as well as a broader sense of economic and political malaise.

At least 59 people died in Egypt's most recent wave of street violence, ignited by the second anniversary of the uprising that toppled Hosni Mubarak from power.

Tunisian authorities said it was not clear who killed Chokri Belaid. But many of the thousands of protesters who poured onto the streets after his death vented their fury against Islamists. (Additional reporting by Omar Fahmy; Editing by Tom Perry and Jon Hemming)